Diploma with honor in teaching physics and mathematics (1986) at the Sukhomlynskyi National University, Mykolaiv, Ukraine (UkrSSR). PhD in Mathematics (1992) at the Mechnikov National University, Odessa, Ukraine. Doctoral dissertation (2022) in theoretical mechanics at the Keldysh Institute of Applied Mathematics of RAS, Moscow, Russia. 1992-1995 Head of Information Science and Computational Technique Department, Faculty of Physics and Mathematics, Sukhomlynskyi National University, Mykolaiv, Ukraine. 1995-2009 Head of Information Science & Mathematical Modeling Department at Volgograd State University, Volzhsky, Volgograd region, Russia. 2009-2022 Senior Researcher at the Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Mathematical Department, Moscow, Russia. 2013-2023 Associated Professor at the Moscow Institute of Physics and Technology (National University), Department of Theoretical Mechanics, Dolgoprudny, Russia.
Biographical Data
Main areas of research
Over the past 15 years I have carried out many investigations connected with Hamiltonian mechanics, Hamiltonian normal form and its applications to problems of periodic solutions investigation for some problems of Celestial Mechanics and to some problems of Lyapunov and formal stability of stationary and periodic solutions. Another trend of my research activities is resolution of singularities in algebraic and differential equations by computer algebra and power geometry technique.
Selected publications
- Batkhin A., Petrov A. Orthogonal-symplectic matrices and their parametric representation // Journal of Symbolic Computation 127 (2025), P. 102353
- Batkhin A.B. Computation of homological equations for Hamiltonian normal form // Recent Trends in Formal and Analytic Solutions of Diff. Equations. V. 782, AMS, 2023. P. 7–20. (Contemporary Mathematics).
- Bruno A.D., Batkhin A.B. Asymptotic forms of solutions to system of nonlinear partial differential equations // Universe. 2023. Vol. 9, no. 1.
- Batkhin A.B. Invariant Coordinate Subspaces of Normal Form of Hamiltonian System // Formal and Analytic Solutions of Differential Equations / ed. by G. Filipuk, A. Lastra, S. Michalik. Singapure : World Scientific, 2022. P. 87–104
- Bruno A.D., Batkhin A.B. Survey of Eight Modern Methods of Hamiltonian Mechanics // Axioms. 2021. Vol. 10, no. 4.
- Batkhin A.B. Bifurcations of periodic solutions of a Hamiltonian system with a discrete symmetry group // Programming and Computer Software. 2020. Vol. 46, no. 2. P. 84–97.
- Batkhin A.B., Batkhina N.V. Henon’s generating solutions and the structure of periodic orbits families of the restricted three-body problem // Une vie dédiée aux système dynamiques. Hommage à Michel Hénon / ed. by J.-M. Alimi, R. Mohayaee, J. Perez. Hermann Editeurs Paris, 2016. P. 45–54.
- Batkhin A.B. Web of families of periodic orbits of the generalized Hill problem // Doklady Mathematics. 2014. Vol. 90, no. 2.P. 539–544.
- Batkhin A. B. Symmetric periodic solutions of the Hill’s problem. I, II // Cosmic Research. — 2013. Vol. 51, no. 4, 6. P. 275–288, 452–464.
- Batkhin A.B., Bruno A.D., Varin V.P. Stability sets of multiparameter Hamiltonian systems // Journal of Applied Mathematics and Mechanics. 2012. Vol. 76, no. 1. P. 56–92.
